Digital balancing of systems with backlash

In the paper the dynamics of an inverted pendulum on a cart is investigated assuming backlash and time delays. The upper equilibrium of the pendulum is stabilized by control force which is provided by a motor driving the wheels of the cart through an elastic teeth belt. The contact between the teeth of the gear (rigid) and the belt (elastic) introduces a nonlinearity known as "backlash" and causes the oscillation of the controlled pendulum around its upper equilibrium.